Math Worksheet · Grades 3–5

Congruent and Similar Shapes Worksheet

A 3-page congruent-and-similar-shapes worksheet for grades 3-5. Students decide whether each pair of shapes is CONGRUENT, SIMILAR, or NEITHER in Section A, complete 6 definition fill-ins in Section B, then solve 3 reasoning word problems in Section C (including the photo-enlargement and all-squares-are-similar classics). Includes a complete answer key.

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Preview of page 1 of the Congruent and Similar Shapes Worksheet

Subject

Math

Grades

Grades 3–5

Skill Focus

Congruent and Similar Shapes, geometry

Lesson Length

20 minutes

Lesson Overview

About this worksheet

Congruent and similar are two of the most-confused terms in elementary geometry, and the worksheet keeps the distinction simple: CONGRUENT means same shape AND same size (a sliding/flipping/turning copy); SIMILAR means same shape but DIFFERENT size (a scaled copy). Every congruent pair is also similar (the ratio is 1 to 1), but most similar pairs are NOT congruent. When two shapes have different SHAPES at all, they are neither congruent nor similar.

The reference box at the top of page 1 teaches the rule and the transformation hint (slide / flip / turn preserves congruence; resize preserves similarity but not congruence), then works through a single example: a square with side 3 inches and a square with side 6 inches are similar (same shape) but not congruent (sizes differ). The (3, 6) pair does NOT appear in any assessed item.

Section A on page 1 has 8 shape-pair items. Five items use rectangles or squares with explicit dimensions (5 vs 5, 4 vs 8, 6×4 vs 6×4, 4×6 vs 8×12, 4×6 vs 6×4) so students can compare numerically. Two items test edge cases: same-angle-different-side triangles are SIMILAR by the AA criterion (item 7), and a rotated rectangle (4×6 vs 6×4) is still CONGRUENT because rotation preserves size (item 6). One item is a NEITHER (circle vs triangle, item 3) so students cannot pattern-match. Section B on page 2 has 6 definition fill-ins.

Section C on page 2 has 3 reasoning word problems with work boxes (1.10in): two triangles with sides 5-12-13 (both congruent AND similar), a 4×6 photo enlarged to 8×12 (similar, ratio 1 to 2), and the famous ‘are all squares similar to each other’ question (yes – 4 right angles + 4 matching sides means the ratio is always fixed). Page 3 is a complete answer key.

How to Use This Lesson

Project the page-1 reference and read both definitions out loud: CONGRUENT = same shape AND same size; SIMILAR = same shape but DIFFERENT size.

Walk through the (3-inch square, 6-inch square) worked example; show that the ratio of sides is 1 to 2, which makes them similar but not congruent.

Work Section A item 1 (two squares, both side 5 cm) together; ask what changes when both squares have the SAME side length (congruent).

Walk through Section A item 6 (rectangle 4 by 6 and rectangle 6 by 4) since the rotation case is the most counter-intuitive (congruent, not just similar).

Assign the rest of Section A independently; remind students to check SAME SHAPE before checking SAME SIZE.

Read Section B item 13 (‘most similar shape pairs are not ____’) together; have students explain why the answer is CONGRUENT.

Use Section C item 17 (all squares are similar to each other) as a closing discussion to anchor the AA / matching-angles rule.

Use the answer key on page 3 for self-check or aide spot-check.

Printable Resource

A classroom-ready PDF with everything in one printable resource.

Full Member Resource · Printable PDF · 3 pages · Answer Key